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Positive Solutions for (n − 1,1)‐Type Singular Fractional Differential System with Coupled Integral Boundary Conditions

Author

Listed:
  • Ying Wang
  • Lishan Liu
  • Xinguang Zhang
  • Yonghong Wu

Abstract

We study the positive solutions of the (n − 1,1)‐type fractional differential system with coupled integral boundary conditions. The conditions for the existence of positive solutions to the system are established. In addition, we derive explicit formulae for the estimation of the positive solutions and obtain the unique positive solution when certain additional conditions hold. An example is then given to demonstrate the validity of our main results.

Suggested Citation

  • Ying Wang & Lishan Liu & Xinguang Zhang & Yonghong Wu, 2014. "Positive Solutions for (n − 1,1)‐Type Singular Fractional Differential System with Coupled Integral Boundary Conditions," Abstract and Applied Analysis, John Wiley & Sons, vol. 2014(1).
    • Handle: RePEc:wly:jnlaaa:v:2014:y:2014:i:1:n:142391
    DOI: 10.1155/2014/142391
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    References listed on IDEAS

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    1. Rui Li & Haoqian Zhang & Hao Tao, 2013. "Unique Solution of a Coupled Fractional Differential System Involving Integral Boundary Conditions from Economic Model," Abstract and Applied Analysis, John Wiley & Sons, vol. 2013(1).
    2. Yuji Liu & Juan J. Nieto & Óscar Otero-Zarraquiños, 2013. "Existence Results for a Coupled System of Nonlinear Singular Fractional Differential Equations with Impulse Effects," Mathematical Problems in Engineering, Hindawi, vol. 2013, pages 1-21, April.
    3. Wenning Liu & Xingjie Yan & Wei Qi, 2014. "Positive Solutions for Coupled Nonlinear Fractional Differential Equations," Journal of Applied Mathematics, John Wiley & Sons, vol. 2014(1).
    4. Jinhua Wang & Hongjun Xiang & Zhigang Liu, 2010. "Positive Solution to Nonzero Boundary Values Problem for a Coupled System of Nonlinear Fractional Differential Equations," International Journal of Differential Equations, Hindawi, vol. 2010, pages 1-12, July.
    5. Xinguang Zhang & Cuiling Mao & Yonghong Wu & Hua Su, 2014. "Positive Solutions of a Singular Nonlocal Fractional Order Differential System via Schauder’s Fixed Point Theorem," Abstract and Applied Analysis, John Wiley & Sons, vol. 2014(1).
    6. Rui Li & Haoqian Zhang & Hao Tao, 2013. "Unique Solution of a Coupled Fractional Differential System Involving Integral Boundary Conditions from Economic Model," Abstract and Applied Analysis, Hindawi, vol. 2013, pages 1-6, August.
    7. Wenning Liu & Xingjie Yan & Wei Qi, 2014. "Positive Solutions for Coupled Nonlinear Fractional Differential Equations," Journal of Applied Mathematics, Hindawi, vol. 2014, pages 1-7, May.
    8. Xinguang Zhang & Cuiling Mao & Yonghong Wu & Hua Su, 2014. "Positive Solutions of a Singular Nonlocal Fractional Order Differential System via Schauder’s Fixed Point Theorem," Abstract and Applied Analysis, Hindawi, vol. 2014, pages 1-8, May.
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